For example, for \(c=1\)  we have \(T_1(n)=O(1)\)  since we do not have to maintain anything. For \(c=2\) , the data structure is required to maintain some bridge
of \(G\)  and it is known that \(T_2(n)=O((\log {n}\cdot \log \log {n})^2)\)  [1]}. For \(c\ge 3\) , in turn, we
have \(T_c(n)=O(n^{1/2}\operatorname{poly}{(c)})\)  [2]}.
